Asymptotic Analysis of Quasi-Equilibrium Glide in Lifting Entry Flight

Abstract

The physical phenomenon of near equilibrium glide in entry flight of a lifting vehicle has long been a very useful utility in flight mechanics analysis and entry guidance designs. But no rigorous mathematical characterization of this quasi-equilibrium flight condition exists that can help provide a deeper understanding of when and how such a flight condition takes place and what is the precise relationship between exact and quasi-equilibrium glide. We present a formal analysis to quasi-equilibrium entry flight in this paper. We embed the quasi-equilibrium gliding flight problem in a class of regular perturbation problems and obtain solutions in asymptotic expansions. We show that the zeroth-order solution is an exact equilibrium glide solution. We provide the complete solution structure and convergence analysis. Our analysis yields quantitative accuracy estimates to the quasi-equilibrium glide condition that can guide how this approximation can be best used. The solution structure we obtain naturally leads to what can be done to improve the accuracy of the quasi-equilibrium glide condition.